Log in to StudySoup
Get Full Access to College Algebra - 9 Edition - Chapter 7 - Problem 14
Join StudySoup for FREE
Get Full Access to College Algebra - 9 Edition - Chapter 7 - Problem 14

Already have an account? Login here
Reset your password

Answer: In Exercises 1114, write the system of linear

College Algebra | 9th Edition | ISBN: 9781133963028 | Authors: Ron Larson ISBN: 9781133963028 204

Solution for problem 14 Chapter 7

College Algebra | 9th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
College Algebra | 9th Edition | ISBN: 9781133963028 | Authors: Ron Larson

College Algebra | 9th Edition

4 5 1 322 Reviews
Problem 14

In Exercises 1114, write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve the system. (Use variables and if applicable.) 1008100112711

Step-by-Step Solution:
Step 1 of 3

Phylum Lycophyta - Club Moss Phylum Lycophyta - club moss, qillworts, Selaginella 1,500 species, from Greek lycos = wolf - club moss, quillwort, Lycopodium, Selaginella Lycophytes are a sister group to ferns and other fern allies (monilophytes) Only five living genera, but for 400 my they were the dominant vegetation on Earth Now reduced to small plants on the forest floor Tropical species are mostly epiphytes (plants that grow on other plants) Temperate species grow in forest understory in small clusters Club mosses (Lycopodiales) are homosporous Selaginella and Isoetes are heterosporous Heterosporous plants - gametes always come from two different gametophytes Homosporous can be same or different gametophytes Heterosporous plants are superior - increased variation for natural selection Club mosses, Selaginella, have sporophylls organized into strobili Cones falls to the ground when ripe, releases spores Gametophytes are independent, free living, look nothing like the parent plant Some species have autotrophic gametophytes, some have heterotrophic gametophytes Phylum Sphenophyta – Horsetails Phylum Sphenophyta - horsetails 25 species, from Greek sphen = wedge - horsetails, Equisetum Closely related to ferns Equisetum is the only surviving genus of this Phylum Equisetum may be the oldest living plant genus on Earth Grows in waste places like roadside ditches or beside railroad tracks, a small and insignificant plant dreaming of former glory Evolved in the late Devonian, Equisetum was a dominant forest tree for several hundred million years Horsetails reached 30-60 ft. tall Leaves are little more than flattened stems Hollow stems are ribbed, jointed, whorl of leaves arise at each joint Stems feel very rough to the touch Pioneer women used them as scouring pads, hence the common name “scouring rush” Epidermal tissues are impregnated with tiny grains of silica (sand) - Why Well defended against herbivores Highly branched vegetative stalks (look like a horse’s tail) Unbranched reproductive stalks, tipped with a large strobilus bearing sporangia Homosporous spores dispersed by elaters, develop into a tiny green gametophyte Phylum Psilophyta - Whisk Ferns Phylum Psilophyta - whisk ferns 2 living genera, from Greek psilo = smooth - whisk ferns, Psilotum life cycle! terms for ferns diagram Closely related to ferns Resemble the first vascular plants (convergent) Once large and widespread group of early land plants, now nearly extinct Only living vascular plants that lack true leaves or true roots (secondary loss) Found in tropical, subtropical habitats (southern US), common weed in greenhouses Small sporangia are bright yellow, form along the upper stems Gametophytes are tiny thread-like plants that lack chlorophyll, look like tiny fungi Phylum Pterophyta – Ferns 12,000 species, from Greek pteridion = little wing - ferns, Pteris, Polypodium, Polytrichum Evolved in the Devonian, share a common ancestor with whisk ferns Abundant and diverse, especially in the tropics (75% of species) Range in size from 1 cm to trees 24 meters tall, with 5 meter fronds Ferns are important in garden industry, florist trade Many herbal remedies derived from ferns Many fern species are edible (fiddleheads) Fern leaf blade is called a frond, leaflets are called pinnae Some ferns have separate fertile stalks which bear the sporangia Most ferns develop sporangia on the underside of their leaves Clusters of sporangia are called sori (sorus) Sorus often protected by an umbrella-like structure called an indusium (-ia) Ferns are mostly homosporous, though some are heterosporous Spores are ejected by the sporangium, which acts like a miniature catapult Outer surface of the sporangia have thick and thin-walled cells Dry out at different rates, builds up enormous tension Top pulls back, reaches a critical point, snaps forward at incredible speeds, one of the most explosive acts in nature Diploid zygote develops into sporophyte Haploid spores formed by meiosis Spores germinate into a tiny heart-shaped autotrophic gametophyte called a prothallus Archegonia and antheridia on upper surface - archegonia at the notch of the heart, antheridia near the rhizoids Sperm swims across to reach the egg Sporophyte grows out of the archegonia Early stage is called a fiddlehead, curled frond gradually unfurls and spreads out Seed Plants – Gymnosperms &Angiosperms Seed plants break the last link with the water - first fully terrestrial plants Sperm no longer needs water to reach egg Seeds keep embryos from drying up Seeds can be modified for dispersal The evolution of the seed is analogous to the evolution of the amniotic egg Both egg and seed provide a time capsule of food and water to the tiny embryo, protecting it from harm Seeds also let the embryo remain dormant until conditions are right for germination Seed plants also no longer rely on flagellated sperm to reproduce The entire male gametophyte (pollen grain) moves through the air to reach the egg Pollen grain is carried by wind, water, animals - pollination All adult sporophytes of seed plants bear sporangia in a strobilus (pine cone, flower) Sporangia of seed plants, like those of primitive plants, produce haploid spores by meiosis All seed plants are heterosporous Spores develop from a spore mother cell Microspores develop in a microsporangia, from a microspore mother cell Megaspores develop in a megasporangia, from a megaspore mother cell Spores develop into tiny gametophytes, smaller than those of ferns and fern allies Microspores develop into male gametophytes Megaspores develop into female gametophytes Seed plants are the final stage in the long transition in alternation of generations The sporophyte is the dominant stage in seed plants, gametophytes greatly reduced Male gametophyte of seed plants now reduced to a few cells (pollen grain), but is still free living and independent Female gametophyte is reduced to a handful of cells, permanently embedded in the tissues of the female sporophyte Megasporangium of seed plants is called a nucellus Megasporangium is covered by a protective layer of cells called an integument Integument is open at one end - micropyle Megasporangium plus the integument is called the ovule* Ovules develop into seeds - integument forms the protective seed coat Seeds plants evolved in the Devonian Primitive plants, like the fern allies, could not compete, and gradually became reduced in size, distribution and importance At the start of the Permian, the last era of the Paleozoic, the fern allies still dominated the planet By the end of the Triassic, the first era of the Mesozoic, seed plants (gymnosperms) were the dominant vegetation on Earth The Jurassic saw the rise of dinosaurs as rulers of the animal world At the same time, gymnosperms rose to dominance of the plant world The domination of the gymnosperms was relatively short-lived By the end of the Mesozoic, they were challenged by the most highly evolved seed plants, the flowering plants or angiosperms Of the 255,000 species of seed plants alive today, only 750 are gymnosperms Gymnosperms Gymnosperms are tracheophytes that develop from seeds, rather than spores Seeds develop from tiny structures called ovules (megasporangium + integument) The ovules of gymnosperms are not entirely enclosed in the tissues of the parent plant Gymnosperm literally means naked seed Phylum Cycadophyta - cycads Phylum Ginkgophyta - Ginkgo biloba Phylum Gnetophyta - Ephedra, Gnetum Phylum Coniferophyta - conifers Gymnosperms – Cycadophyta Phylum Cycadophyta - cycads ~ 100 species, 9 genera, from Greek kyos = palm - cycads Palm-like shrubs and trees, with crown of very thick leaves atop unbranched stems Cycads are dioecious, separate male and female plants Leaves are incredibly well defended Sharp tips on leaves Toxic secondary compounds, including neurotoxins and carcinogens Why Hungry dinosaurs! Reached their peak during the Mesozoic, the Age of Cycads, 6 - 60 ft. tall! Pollen sacs and ovules in scale-like cones Microsporangiate cones - male Megasporangiate cones - female Cones are often very large in relation to the plant (unlike pine cones) Wind pollinated, strategy requires immense amounts of airborne pollen to get lucky Early cycads may have attracted beetles to pollinate them, beetles like to eat pollen (high in protein) May be the beginning of animal pollination, successfully exploited by flowering plants Only one species native to the US - Zamia pumila, found in southern Florida Seminoles eat the starchy roots Popular ornamental - expensive, extremely slow growing, lives 1,000 years or more Sago flour from cycad stems (sometimes palms), popular in India, Japan, Sri Lanka Symbiotic with nitrogen fixing cyanobacteria Gymnosperms – Ginkgophyta Phylum Ginkgophyta - Ginkgo biloba 1 Species (!) - Ginkgo biloba - maidenhair tree Sole surviving species cultivated for centuries by the Chinese and Japanese - may no longer exist in the wild Species name comes from leaves - two lobes, very different from typical gymnosperm Ginkgos and cycads show transitional stage in seed plant evolution Ginkgos and cycads have flagellated sperm Male gametophyte grows a long pollen tube, an extension of its body through which the sperm can swim to the egg Tiny female strobili contain megasporangia Microsporangia form small cones, hang down like tiny pine cones Seeds are covered with a fleshy coat Incredible odor when ripe - rotten dog vomit !! Trees are popular for bonsai Seeds used in herbal medicine by ancient Chinese - currently very popular Attractive shade trees, up to 100 ft. tall, resistant to air pollution and insects, bright yellow foliage in the Fall importance - economic seeds used in herbal medicine by ancient chinese attractive shade trees, 100 ft tall, resistant to air pollution Gymnosperms – Gnetophyta Phylum Gnetophyta - Ephedra 70 species, 3 genera - Ephedra, Gnetum, Welwitschia Odd little group of xerophytes - plants adapted to arid conditions Once thought to be the closest common ancestor to flowering plants Many species produce nectar to attract insects for pollination Ephedra has double fertilization (more later), like angiosperms Only gymnosperms with vessels in addition to tracheids Gnetum even looks very much like modern angiosperm tree Molecular analysis suggests otherwise Gnetophytes now thought to be closely related to the conifers, or perhaps a sister group to all the other gymnosperms Ephedra, like whisk fern, is a “stem plant”, photosynthetic stem with no leaves most important Common in deserts of theAmerican West and Mexico, grows everywhere exceptAustralia Welwitschia looks like it came from another planet Welwitschia grows in the deserts of southwesternAfrica Squat cup-shaped stem above the soil, most of the plant is underground Only two strap-shaped leaves, which live 100 years or more, get torn into many strips Male and female strobili grow from the edges of the upper stem Ephedra is the source of the drug ephedrine One of the oldest medicinal plants - in use for over 5,000 years Used to treat sinus problems, hay fever, headaches, asthma Pseudoephedrine is a synthetic version of ephedrine used in sudafeds Gymnosperms – Coniferophyta Phylum Coniferophyta - conifers 550 species in 50 genera, from Greek conus = cone, ferre = to bear - pines, spruces, firs, hemlocks, yews, redwoods, cypress Ancient group, evolved ~ 290 mya (Permian) Conifers are the only gymnosperms that are still successful competitors with angiosperms Conifers evolved in a cool, dry period Conifers evolved special water-conducting cells called tracheids Tracheids are much more efficient in overcoming water stress (dry periods) Needle shaped leaves are also an adaptation to conserve water Needles emerge in small bundles from a greatly shortened branch tip Conifers are still the best competitors today in cool, dry habitats on high latitudes, high elevations, sandy soils Most conifers are evergreen Exceptions are the larch and the bald cypress, which are deciduous Conifers are the longest-lived plants on the planet Record holder is a bristlecone pine estimated at 4,900 years old! Some may be over 7,000 years old Sporophytes produce sporangia on cone-shaped strobilus (pine cone) - male (pollen cones) and female (seed cones) Male and female cones on the same tree, but not same time, don’t fertilize themselves Female cones are large and conspicuous, male cones are ephemeral and puny Afew conifers, like juniper, yews, and Podocarpus (locally common landscape tree) have seeds with a fleshy coating, look like little berries All parts of the Podocarpus tree, especially the seeds, are toxic! Male cone is smaller, bears microsporangia Microsporangia contain microspore mother cells Mother cells divide by meiosis to form haploid microspores Microspores develop into the male gametophyte, the pollen grain Each scale of the male cone (pollen cone) is a sporophyll with two microsporangia on its lower surface Pollen cones open to shed pollen in large quantities - major source of allergies Wings on pollen - seed dispersal - may help grain float up to the micropyle Female cone is larger, bears megasporangia Megaspore mother cell produces four haploid megaspores by meiosis Three megaspores degenerate Remaining megaspore develops into the female gametophyte Female gametophyte consists of two archegonia, with an egg in each Ovulate cones open to receive pollen ( gymnos = naked seed), then close again Pollen grain lands on cone, grows long pollen tube, takes up to 15 months to reach the archegonia (long engagement) Pollen tube enters the female gametophyte through an opening called the micropyle Nucleus divides in two, pollen tube discharges the two “sperm nuclei” One sperm fertilizes the egg, the other sperm degenerates Seeds develop in the megasporangium, two seeds atop each scale (sporophyll) Part of the sporophyll detaches as a tiny wing to help disperse the mature seed Conifer seeds are a very important source of food for wildlife Conifer seeds are complex little critters -includes cells from three generations (!) Nutritive tissues inside the seed are the body cells of the female gametophyte Seed coat from the body of the parental sporophyte Embryo is the next sporophyte generation Lumber - furniture industry, housing, tools, sailing ships Pitch, tars, resins, turpentine - used in warfare, perfumes, jewelry (amber), waterproofing ships Christmas trees!! Angiosperms - Flowering Plants Charles Darwin called the evolution of the angiosperms “an abominable mystery” The evolution of angiosperms remains a mystery to this day Flowering plants evolved sometime during the Cretaceous, while the dinosaurs were at their peak Water lilies one of the first clades to evolve They quickly became the dominant plants, although gymnosperms continue to rule in cold, dry, or sandy habitats Oldest known angiosperm (recently discovered) isArchaefructus, ~ 122-145 my (upper Jurassic), discovered in mainland China in 2002 Most primitive living angiosperm (also recently discovered) is Amborella Grows as a shrub or small tree on South Pacific island of New Caledonia Angiosperms - DivisionAnthophyta More than 255,000 species of flowering plants grouped in over 300 families Flowering plants are superior competitors Able to survive in a greater variety of habitats Mature more quickly Produce greater number of seeds Flowering plants are superior competitors Fruit for seed dispersal Wider-bore vessels to conduct water Animals aid in pollination - can survive as small scattered populations, whereas wind-pollinated species need dense populations More diverse and specialized group Gymnosperms are woody perennials, angiosperms can be perennials or annuals Leaves are thin blades, diversity of shapes Woody tissues are more complex and highly specialized Angiosperms - Economic Importance Food - fruits, vegetables, grains, nuts, spices fruit - from pistol vegetable - technically no such thing as a veggie Wood - homes, tools, ships… Oils and waxes - olive oil, perfumes, soap… Drugs - coffee, chocolate, wine, beer… Medicines - quinine, digitalis, codeine… All angiosperms have flowers Flowers are reproductive structures that are formed from four sets of modified leaves Amazing diversity of floral structure Linnaeus used these differences in his first attempt at classifying plants Angeios = Greek for vessel (container) Ovules are encased in an ovary, not lying naked on the scales of a strobilus, as they are in gymnosperms Ovules in the ovary develop into seeds The ovary walls form a fruit to help disperse the seeds Fruit is a marvelous example of coevolution between plants and animals Coevolution occurs when an evolutionary change in one organism leads to an evolutionary change in another organism that interacts with it Flowering plants show two great examples of coevolution Evolution of fruit dispersal Evolution of animal pollination Fruits function to disperse seeds Animals eat fruit, but don’t digest seeds Tiny hooks and spines to attach to animal Also dispersed by wind, water (coconuts) Flowers that rely on wind pollination are tiny and inconspicuous (like oak trees, maple trees, corn, grasses) Flowers that are pollinated by animals have showy petals to attract the pollinators Flowers advertise their reward of nectar, sugar water to attract pollinators Nectar contains sugar (sucrose, fructose or glucose), amino acids, vitamins, oils etc. Made by glands called nectaries, usually near the base of the ovary Nectar sipped by bees is the sugar source for honey! Flowering plants go to great lengths to avoid pollinating themselves Chemical – Pollen and ovule are chemically incompatible Architectural – Stamens and pistils are arranged to avoid contact Temporal – Pollen and pistil mature at different times Flowers consist of four sets of modified leaves on a shortened stem Sepals - protect floral parts in the bud Petals - attract pollinators Stamens - anthers and filaments Carpels - form the pistil (stigma, style, ovary) phone for pic ophrys apifera (cool plant that attracts wasps) What the heck is a carpel Cut into the pistil and you will see one or more tiny chambers, each chamber holding one or more sporangia on tiny stalks These sporangia are the ovules - each carpel can hold one or several ovules Goethe, German writer, philosopher, and (in his spare time) noted botanist, proposed that carpels evolved from leaves Chambers in the pistil were probably formed from a sporophyll Edges of the leaf folded over and fused together to form a protective chamber Goethe’s “foliar theory of the carpel” is still the best hypothesis for explaining the evolution of the carpel Sporophylls are leaves modified to hold spores Carpels are leaves modified to hold seeds What we are used to calling the pistil consists of the fusion of several carpels along the midrib of the modified leaves The root “carp” means fruit – appropriate, this portion of the flower becomes the fruit Sporophytes form sporangia Stamens are highly modified sporophylls Sporangia are located on the stamens, inside the anthers, atop a slender filament Each anther holds four microsporangia - microspores develop in microsporangia Microspore mother cell divides by meiosis to form four haploid microspores Each microspore develops into a multicellular pollen grain Pollen grains are the male gametophytes Microspore divides into a tube cell (will form pollen tube) and a sperm cell (nucleus will act as sperm) Mature male gametophyte is teeny-tiny, only a few cells Cross walls between two pairs of microsporangia break down Results in two long pollen sacs full of developing gametophytes Pollen grain are wrapped in sporopollenin, the same biopolymer that protects spores Surface of pollen grains can be very complex, species specific patterns - floral thumbprint Pollen shapes are critical for flowers - lets them recognize pollen of their own species Pollen in fossil record also allows us to reconstruct ancient environments Meanwhile, inside the ovary…. Sporophytes form sporangia Megaspores develop in megasporangia Megasporangia are located in the ovary, at the base of the pistil Each pistil consists of one or more carpels (modified leaves - sporophylls) Each carpel holds one or more ovules Ovules = megasporangium + integument Ovules are attached to the walls of the ovary by a short stalk (just like babies) Each ovule (megasporangia) will ultimately contain a single egg Megaspore mother cell divides by meiosis to form four haploid megaspores Three megaspores degenerate, the fourth divides by mitosis three times to form 8 haploid nuclei This large cell with 8 nuclei is the female gametophyte, called the embryo sac* Weird cellular square dance ensues… One nucleus from each group of four now migrates to the center of the embryo sac Remaining three nuclei in each group migrate to each pole Cell walls form around the the three nuclei Female gametophyte now consists of 7 cells, 3 at the top, 3 at the bottom, 1 large cell in the middle with two nuclei One of the bottom 3 cells will act as the egg Pollen grain reaches the stigma of the pistil, grows a long tube (pollen tube) to penetrate the neck of the pistil and reach the ovary As the pollen tube approaches the embryo sac, the sperm nucleus divides in two, mature male gametophyte now contains three nuclei - two sperm nuclei, one tube Pollen tube enters the micropyle, discharges the sperm nuclei into the embryo sac Two central female nuclei fuse together to make a 2N nucleus One sperm nucleus fuses with the 2N nucleus to make a 3N nucleus - the other sperm nucleus fertilizes the egg Embryo sac now contains a diploid zygote, which will grow up into an adult sporophyte Also contains a 3N nucleus, which begins to divide repeatedly, forms the nutrition for the embryo - called endosperm (seed within) This process is called double fertilization, and it is unique to angiosperms Ephedra has double fertilization, suggesting that gnetophytes are related to angiosperms, but Ephedra doesn’t form endosperm Ovule = megasporangium + integuments Megasporangium holds developing embryo Integument develops into a hard protective jacket, the seed coat, which protects the embryo from dessication and mechanical damage Walls of the ovary develop into the fruit Each section of orange, each chamber in the tomato is a carpel, now filled with little embryos inside seeds Ecosystems and Energy The large fish eat the small fish; The small fish eat the water insects; The water insects eat plants and mud Large fowl cannot eat small grain One hill cannot shelter two tigers These three ancient Chinese proverbs preface a chapter in Animal Ecology (1927) The author, Charles Elton, was a young British ecologist Elton took a radically different approach to understanding animal communities Prior to Elton, ecology was a purely descriptive science To understand the community, you merely had to catalog its organisms In the great European tradition, natural history consisted mostly of collecting stuff Once you had collected it, named it, and put it away in a museum, your job was done Great museum collections, cabinets of curiosities, were very popular with Victorians Elton claimed it was not enough to tally names and numbers To understand a biological community, you had to understand the functional relationships between its organisms Biological community = all the organisms that appear in a particular habitat that interact with one another What was most important in a community, said Elton, was not who you were, but what you did Niche = functional role of an organism in an ecosystem (ex. nocturnal insectivore – bat, niche = job, habitat = address) Elton wrote “When an ecologist says ‘there goes a badger’, he should include in his thoughts some idea of the animal’s place in the community, just as if he had said ‘there goes the vicar.” Elton was a pioneer - trying to learn the forces that determine which organisms, and how many of them, can live in a particular ecosystem While a student at Oxford, Elton went on an expedition to Bear Island, a tiny island in theArctic Sea, near Spitsbergen, north of northern Norway (!) Elton mapped out the feeding relationships on the island, published as part of his first important paper on community structure Community structure = how many different species in the community + how many individuals of each different species What determines community structure Long standing debate in ecology - is it predation, competition, food Elton felt strongly that food was the most important factor in shaping community structure - who or what you ate, who or what ate you… Elton first described the food chain and the food web (what he called the food cycle) Food chain = linear sequence of predator and prey in an ecosystem (who eats who) Food web = interconnection of all the food chains in an ecosystem The large fish eat the small fish; The small fish eat the water insects; The water insects eat plants and mud This ancient proverb describes a simple food chain Food chains represent the flow of energy through an ecosystem Food chains are a sequence of producers and consumers, prey and predators Large fowl cannot eat small grain Elton was struck by the fact that all the animals on Bear Island came in discrete sizes, much bigger or smaller than others Elton was struck by the fact that all the animals on Bear Island came in discrete sizes, much bigger or smaller than others Larger the animals, the scarcer they were Why did life form a Pyramid of Numbers Why were big fierce animals rare Why should life come in discrete sizes Answer to this dilemma was not proposed until 1942 Raymond Lindeman, young aquatic ecologist at the University of Minnesota Lindeman realized that ecosystems were systems that transformed energy Ecosystem = all of the biological communities in a given area together with their physical habitat Energy flows through ecosystems As energy passes from one trophic level to the next (feeding level), some energy is lost at each level Herbivores eat plants, change the plant’s energy into their own energy Predators eats herbivores, incorporate the energy of the prey into parts of the predator Herbivores eat plants, change the plant’s energy into their own energy Predators eats herbivores, incorporate the energy of the prey into parts of the predator This transformation of energy is always inefficient - simple thermodynamics Amount of energy left in the system decreases at each level Some locked up in maintenance and reproduction on each level Some lost from predator wastage (stems, bones) Some lost as heat energy, burned up in metabolic conversion - no reaction is 100% efficient Elton’s Pyramid of Numbers is explained by Lindeman’s Pyramid of Energy

Step 2 of 3

Chapter 7, Problem 14 is Solved
Step 3 of 3

Textbook: College Algebra
Edition: 9
Author: Ron Larson
ISBN: 9781133963028

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Answer: In Exercises 1114, write the system of linear